Venetian white is lead white, and Venetian white in particular is closely related to the horror stories of people using lead white, PW1 as a cosmetic. Apparently the Venetian variety of ceruse or lead white was thought at the time to be a superior quality and was marketed as a face whitener, which of course had ghastly results and in some cases led to death. More on that may be found here. According to Wikipedia, the same Venetian white which was used in cosmetics was also used by painters at the time, and was thought to be high quality.
Centuries later, in the mid-1800s, George Field wrote of "Venetian White," which was a blend of lead white (lead carbonate) with barite. Taking inspiration from this 19th century version, Natural pigments offers a Venetian White as a mix of lead white with barite. Source here.
Natural Pigments has also been involved in lightfastness testing for oil colors. Though not much can be definitively said in regard to the topic in question, some preliminary research from Natural Pigments/ Rublev suggested that barite may cause some darkening in certain contexts, however how that interacts with lead white specifically is unclear.
For more information, Stack Lead White and the page on PW1 contain additional details.
